The objective of this proposal is the development and evaluation of statistical methods for use in research related to understanding the natural history of Acquired Immunodeficiency Syndrome (AIDS). A collaborative team from University of California Berkeley, and the University of California, San Francisco, will be involved in the project. Three topics will be of specific interest. The first relates to detailed analysis of methods for the use of data on incidence of AIDS to provide estimates of the distribution of time to Human Immunodeficiency Virus (HIV) infection and estimates of the incubation period distribution. The second is concerned with methodology for estimation of properties of infectivity of the virus associated with various kinds of contacts based on data on the number of contacts and infection status of partners of known infected individuals. Of particular interest are statistical techniques which handle issues including lack of information on the dates of infection of either partner and which elucidate patterns of change in infectiousness of infected individuals over the period from infection to onset of AIDS. Finally, further methodological work is proposed relating to marker variables which evolve during incubation and measure in part the decline of the immune system,. Statistical models are necessary to make full use of these variables in such ways as surrogate responses for onset of AIDS in clinical trials, correlates for times of infection when these are known, particularly for prevalent samples, and in understanding their role in the hazard of onset of AIDS. All methods will be applied to various data sets where appropriate. This part of the project will include statistical work on the construction of markers and evaluation of marker models on data arising from follow-up cohorts of infected individuals.